Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.g.j.449.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.44949i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.224745 | − | 2.22474i | 0.100509 | − | 0.994936i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.449490i | − | 0.124666i | −0.998055 | − | 0.0623330i | \(-0.980146\pi\) | ||
0.998055 | − | 0.0623330i | \(-0.0198541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.44949 | + | 0.550510i | 1.40705 | + | 0.142141i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.44949 | 1.47961 | 0.739807 | − | 0.672819i | \(-0.234917\pi\) | ||||
0.739807 | + | 0.672819i | \(0.234917\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.44949 | 0.534522 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.89898i | 1.43854i | 0.694732 | + | 0.719268i | \(0.255523\pi\) | ||||
−0.694732 | + | 0.719268i | \(0.744477\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89898 | − | 1.00000i | −0.979796 | − | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89898 | −0.538327 | −0.269163 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269163 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.898979 | −0.161461 | −0.0807307 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807307 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 12.0000i | − | 2.08893i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.22474 | − | 0.224745i | −0.376051 | − | 0.0379888i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10102 | 0.176304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8990 | −1.70213 | −0.851067 | − | 0.525057i | \(-0.824044\pi\) | ||||
−0.851067 | + | 0.525057i | \(0.824044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.89898i | 1.35708i | 0.734563 | + | 0.678541i | \(0.237387\pi\) | ||||
−0.734563 | + | 0.678541i | \(0.762613\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.674235 | + | 6.67423i | −0.100509 | + | 0.994936i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.898979i | − | 0.131130i | −0.997848 | − | 0.0655648i | \(-0.979115\pi\) | ||
0.997848 | − | 0.0655648i | \(-0.0208849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89898 | −0.685994 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.10102i | − | 0.151237i | −0.997137 | − | 0.0756184i | \(-0.975907\pi\) | ||
0.997137 | − | 0.0756184i | \(-0.0240931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.10102 | + | 10.8990i | −0.148462 | + | 1.46962i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.7980i | 2.09249i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.44949 | −0.839652 | −0.419826 | − | 0.907605i | \(-0.637909\pi\) | ||||
−0.419826 | + | 0.907605i | \(0.637909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.44949 | −1.08185 | −0.540923 | − | 0.841072i | \(-0.681925\pi\) | ||||
−0.540923 | + | 0.841072i | \(0.681925\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000i | 0.377964i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | − | 0.101021i | −0.124035 | − | 0.0125301i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.8990 | −2.03440 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8990 | −1.29347 | −0.646735 | − | 0.762714i | \(-0.723866\pi\) | ||||
−0.646735 | + | 0.762714i | \(0.723866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.89898i | 0.807464i | 0.914877 | + | 0.403732i | \(0.132287\pi\) | ||||
−0.914877 | + | 0.403732i | \(0.867713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.44949 | − | 12.0000i | 0.282843 | − | 1.38564i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89898i | 0.558291i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.89898 | 0.326161 | 0.163080 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163080 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44949i | 0.268866i | 0.990923 | + | 0.134433i | \(0.0429214\pi\) | ||||
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.44949 | + | 0.449490i | 0.482615 | + | 0.0487540i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.10102i | − | 0.761309i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.449490 | −0.0471193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.20204i | − | 0.228341i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.44949 | − | 14.3485i | 0.148715 | − | 1.47212i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.79796i | − | 0.385624i | −0.981236 | − | 0.192812i | \(-0.938239\pi\) | ||
0.981236 | − | 0.192812i | \(-0.0617608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.6969 | 1.47710 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.10102i | − | 0.305553i | −0.988261 | − | 0.152776i | \(-0.951179\pi\) | ||
0.988261 | − | 0.152776i | \(-0.0488214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.550510 | − | 5.44949i | 0.0537243 | − | 0.531816i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.89898 | −0.277672 | −0.138836 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138836 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.89898 | 0.464991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.202041i | − | 0.0190064i | −0.999955 | − | 0.00950321i | \(-0.996975\pi\) | ||
0.999955 | − | 0.00950321i | \(-0.00302501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.3485 | + | 1.55051i | 1.43125 | + | 0.144586i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.34847i | 0.124666i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 26.6969i | − | 2.40718i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.32577 | + | 10.6742i | −0.297465 | + | 0.954733i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.10102i | − | 0.452642i | −0.974053 | − | 0.226321i | \(-0.927330\pi\) | ||
0.974053 | − | 0.226321i | \(-0.0726699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.7980 | −1.91920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.55051 | 0.135469 | 0.0677344 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677344 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.44949i | − | 0.559242i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.7980i | 1.52058i | 0.649582 | + | 0.760291i | \(0.274944\pi\) | ||||
−0.649582 | + | 0.760291i | \(0.725056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.44949 | 0.547039 | 0.273519 | − | 0.961867i | \(-0.411812\pi\) | ||||
0.273519 | + | 0.961867i | \(0.411812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.20204 | 0.185445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.20204i | 0.184144i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.651531 | + | 6.44949i | −0.0541067 | + | 0.535601i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.44949i | − | 0.202031i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.7980 | 1.29422 | 0.647110 | − | 0.762397i | \(-0.275978\pi\) | ||||
0.647110 | + | 0.762397i | \(0.275978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.202041 | + | 2.00000i | −0.0162283 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.44949i | − | 0.674343i | −0.941443 | − | 0.337171i | \(-0.890530\pi\) | ||
0.941443 | − | 0.337171i | \(-0.109470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.69694 | 0.213881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.89898 | 0.543716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.8990i | − | 1.32363i | −0.749667 | − | 0.661815i | \(-0.769786\pi\) | ||
0.749667 | − | 0.661815i | \(-0.230214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −26.6969 | − | 2.69694i | −2.07835 | − | 0.209956i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.89898i | 0.379094i | 0.981872 | + | 0.189547i | \(0.0607020\pi\) | ||||
−0.981872 | + | 0.189547i | \(0.939298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7980 | 0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.3485 | −1.47961 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.2474i | 1.38733i | 0.720299 | + | 0.693664i | \(0.244005\pi\) | ||||
−0.720299 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 4.89898i | −0.0755929 | + | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 15.7980i | − | 1.18745i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.79796 | −0.433360 | −0.216680 | − | 0.976243i | \(-0.569523\pi\) | ||||
−0.216680 | + | 0.976243i | \(0.569523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2474 | −1.05900 | −0.529502 | − | 0.848309i | \(-0.677621\pi\) | ||||
−0.529502 | + | 0.848309i | \(0.677621\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.6969i | − | 1.52996i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.44949 | − | 0.449490i | −0.327133 | − | 0.0330471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.79796i | − | 0.716498i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6969 | −1.20815 | −0.604074 | − | 0.796928i | \(-0.706457\pi\) | ||||
−0.604074 | + | 0.796928i | \(0.706457\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.5959i | − | 1.26658i | −0.773914 | − | 0.633291i | \(-0.781704\pi\) | ||
0.773914 | − | 0.633291i | \(-0.218296\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.247449 | − | 2.44949i | 0.0177202 | − | 0.175412i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.10102i | − | 0.648421i | −0.945985 | − | 0.324210i | \(-0.894901\pi\) | ||
0.945985 | − | 0.324210i | \(-0.105099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.10102 | −0.503378 | −0.251689 | − | 0.967808i | \(-0.580986\pi\) | ||||
−0.251689 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5959 | −1.38219 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.89898i | 0.203468i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44949 | + | 24.2474i | −0.171080 | + | 1.69352i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 20.6969i | − | 1.43854i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.5959 | −2.18554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 26.6969i | − | 1.82924i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.7980 | + | 2.00000i | 1.35021 | + | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.898979i | 0.0610267i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.8990 | −1.14193 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.898979 | 0.0604719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6969 | + | 3.00000i | 0.979796 | + | 0.200000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.34847i | 0.487735i | 0.969809 | + | 0.243868i | \(0.0784162\pi\) | ||||
−0.969809 | + | 0.243868i | \(0.921584\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.1464 | 1.00090 | 0.500452 | − | 0.865764i | \(-0.333167\pi\) | ||||
0.500452 | + | 0.865764i | \(0.333167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | −0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.2020i | − | 0.668358i | −0.942510 | − | 0.334179i | \(-0.891541\pi\) | ||
0.942510 | − | 0.334179i | \(-0.108459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | − | 0.202041i | −0.130466 | − | 0.0131797i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.10102i | 0.461261i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.7980 | 1.66873 | 0.834366 | − | 0.551211i | \(-0.185834\pi\) | ||||
0.834366 | + | 0.551211i | \(0.185834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6969 | 1.33321 | 0.666604 | − | 0.745412i | \(-0.267747\pi\) | ||||
0.666604 | + | 0.745412i | \(0.267747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 22.0454i | − | 1.41421i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.224745 | + | 2.22474i | −0.0143584 | + | 0.142134i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.89898i | − | 0.184458i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.55051 | 0.0978673 | 0.0489337 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489337 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 33.7980i | − | 2.12486i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.10102 | + | 10.8990i | −0.0689486 | + | 0.682521i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.6969i | 1.29104i | 0.763744 | + | 0.645520i | \(0.223359\pi\) | ||||
−0.763744 | + | 0.645520i | \(0.776641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.69694 | 0.538327 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.79796i | 0.604168i | 0.953281 | + | 0.302084i | \(0.0976823\pi\) | ||||
−0.953281 | + | 0.302084i | \(0.902318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.44949 | − | 0.247449i | −0.150471 | − | 0.0152007i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.4949i | 1.49906i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1464 | −0.923494 | −0.461747 | − | 0.887012i | \(-0.652777\pi\) | ||||
−0.461747 | + | 0.887012i | \(0.652777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.10102i | − | 0.0666368i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.0000 | + | 4.89898i | 1.44725 | + | 0.295420i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10102i | 0.306491i | 0.988188 | + | 0.153245i | \(0.0489725\pi\) | ||||
−0.988188 | + | 0.153245i | \(0.951028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.69694 | 0.161461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.2474i | 1.67914i | 0.543254 | + | 0.839568i | \(0.317192\pi\) | ||||
−0.543254 | + | 0.839568i | \(0.682808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 35.1464 | + | 3.55051i | 2.08189 | + | 0.210314i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.8990i | 0.643346i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.30306 | 0.545355 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.24745i | − | 0.364980i | −0.983208 | − | 0.182490i | \(-0.941584\pi\) | ||
0.983208 | − | 0.182490i | \(-0.0584157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44949 | + | 14.3485i | −0.0843926 | + | 0.835400i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.10102 | 0.179337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.89898 | 0.512929 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 20.6969i | − | 1.18901i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.89898 | + | 18.7980i | −0.108735 | + | 1.07637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.24745i | − | 0.242415i | −0.992627 | − | 0.121207i | \(-0.961323\pi\) | ||
0.992627 | − | 0.121207i | \(-0.0386766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.59592 | 0.432117 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.5959i | − | 0.994580i | −0.867584 | − | 0.497290i | \(-0.834328\pi\) | ||
0.867584 | − | 0.497290i | \(-0.165672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.67423 | + | 0.674235i | 0.376051 | + | 0.0379888i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 26.4949i | − | 1.48810i | −0.668123 | − | 0.744051i | \(-0.732902\pi\) | ||
0.668123 | − | 0.744051i | \(-0.267098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2020 | 0.795162 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.5959 | −1.09374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8990i | 0.717718i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.449490 | + | 2.20204i | −0.0249332 | + | 0.122147i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.10102i | − | 0.392687i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.898979 | −0.0495623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6969 | −0.587957 | −0.293978 | − | 0.955812i | \(-0.594979\pi\) | ||||
−0.293978 | + | 0.955812i | \(0.594979\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.7980 | + | 1.79796i | 0.972406 | + | 0.0982330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.5959i | − | 1.61219i | −0.591785 | − | 0.806096i | \(-0.701576\pi\) | ||
0.591785 | − | 0.806096i | \(-0.298424\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.494897 | 0.0268791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.40408 | 0.238494 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.79796 | + | 37.5959i | −0.204475 | + | 2.02410i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 19.1010i | − | 1.02540i | −0.858569 | − | 0.512698i | \(-0.828646\pi\) | ||
0.858569 | − | 0.512698i | \(-0.171354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.55051 | −0.190054 | −0.0950272 | − | 0.995475i | \(-0.530294\pi\) | ||||
−0.0950272 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.1010i | − | 0.697297i | −0.937254 | − | 0.348648i | \(-0.886641\pi\) | ||
0.937254 | − | 0.348648i | \(-0.113359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.44949 | + | 24.2474i | −0.130005 | + | 1.28692i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.89898i | 0.259281i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.5959 | −0.612009 | −0.306005 | − | 0.952030i | \(-0.598992\pi\) | ||||
−0.306005 | + | 0.952030i | \(0.598992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.8434i | 1.67134i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3485 | + | 1.55051i | 0.803376 | + | 0.0811574i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000i | 1.67039i | 0.549957 | + | 0.835193i | \(0.314644\pi\) | ||||
−0.549957 | + | 0.835193i | \(0.685356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.6969 | 1.70213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.10102 | −0.0571621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6969i | 1.27876i | 0.768891 | + | 0.639380i | \(0.220809\pi\) | ||||
−0.768891 | + | 0.639380i | \(0.779191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.1464 | − | 8.14643i | −1.35020 | − | 0.420680i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.30306i | 0.0671111i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30306 | 0.0669338 | 0.0334669 | − | 0.999440i | \(-0.489345\pi\) | ||||
0.0334669 | + | 0.999440i | \(0.489345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4949 | 0.640133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.8990i | 0.863498i | 0.901994 | + | 0.431749i | \(0.142103\pi\) | ||||
−0.901994 | + | 0.431749i | \(0.857897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8990 | + | 1.10102i | 0.555463 | + | 0.0561132i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 26.6969i | − | 1.35708i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8990 | 1.16102 | 0.580512 | − | 0.814252i | \(-0.302852\pi\) | ||||
0.580512 | + | 0.814252i | \(0.302852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7980 | −0.697793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.79796i | 0.191582i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.651531 | − | 6.44949i | 0.0327821 | − | 0.324509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3485i | 0.870695i | 0.900263 | + | 0.435347i | \(0.143374\pi\) | ||||
−0.900263 | + | 0.435347i | \(0.856626\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.7980 | 0.790887 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3939 | 1.46786 | 0.733930 | − | 0.679225i | \(-0.237684\pi\) | ||||
0.733930 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.404082i | 0.0201288i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.02270 | + | 20.0227i | −0.100509 | + | 0.994936i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79796i | 0.485667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4949 | 0.716727 | 0.358363 | − | 0.933582i | \(-0.383335\pi\) | ||||
0.358363 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.5959 | −2.15043 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.44949i | 0.317359i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44949 | + | 0.550510i | 0.267505 | + | 0.0270235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7980i | 0.773629i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.44949 | −0.315078 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.7980 | 1.15984 | 0.579921 | − | 0.814673i | \(-0.303083\pi\) | ||||
0.579921 | + | 0.814673i | \(0.303083\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.69694i | 0.131130i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | − | 9.79796i | 0.0970143 | − | 0.475271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.44949i | 0.408899i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.39388 | −0.260419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7980 | 0.857298 | 0.428649 | − | 0.903471i | \(-0.358990\pi\) | ||||
0.428649 | + | 0.903471i | \(0.358990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7980i | 0.951429i | 0.879600 | + | 0.475715i | \(0.157810\pi\) | ||||
−0.879600 | + | 0.475715i | \(0.842190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.7980 | − | 1.59592i | −0.757454 | − | 0.0765184i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 44.4949i | 2.12848i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.3939 | −1.78471 | −0.892356 | − | 0.451332i | \(-0.850949\pi\) | ||||
−0.892356 | + | 0.451332i | \(0.850949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.79796i | − | 0.465515i | −0.972535 | − | 0.232758i | \(-0.925225\pi\) | ||
0.972535 | − | 0.232758i | \(-0.0747749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.24745 | − | 22.2474i | 0.106539 | − | 1.05463i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.6969i | 1.83030i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.3939 | 2.51422 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 48.0000i | − | 2.25524i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.101021 | + | 1.00000i | −0.00473591 | + | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.59592i | − | 0.448878i | −0.974488 | − | 0.224439i | \(-0.927945\pi\) | ||
0.974488 | − | 0.224439i | \(-0.0720550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.65153 | −0.123494 | −0.0617470 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617470 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.5959i | 1.65428i | 0.561994 | + | 0.827141i | \(0.310034\pi\) | ||||
−0.561994 | + | 0.827141i | \(0.689966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.89898 | − | 0.494897i | −0.227185 | − | 0.0229503i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 5.55051i | − | 0.256847i | −0.991719 | − | 0.128423i | \(-0.959008\pi\) | ||
0.991719 | − | 0.128423i | \(-0.0409917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.6969 | 0.953665 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 43.5959i | − | 2.00454i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.5959 | − | 6.44949i | −1.44972 | − | 0.295923i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.30306i | 0.151237i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.6969 | −1.76811 | −0.884054 | − | 0.467385i | \(-0.845196\pi\) | ||||
−0.884054 | + | 0.467385i | \(0.845196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.898979 | −0.0409899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.8990i | 0.768930i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.44949 | − | 0.853572i | −0.383672 | − | 0.0387587i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.6969i | − | 1.66290i | −0.555602 | − | 0.831449i | \(-0.687512\pi\) | ||
0.555602 | − | 0.831449i | \(-0.312488\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.3939 | 1.87190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5959 | 0.884351 | 0.442176 | − | 0.896928i | \(-0.354207\pi\) | ||||
0.442176 | + | 0.896928i | \(0.354207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.79796i | − | 0.261127i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.30306 | − | 32.6969i | 0.148462 | − | 1.46962i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8990i | 0.488886i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7980 | 1.15488 | 0.577438 | − | 0.816435i | \(-0.304053\pi\) | ||||
0.577438 | + | 0.816435i | \(0.304053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.00000i | 0.178351i | 0.996016 | + | 0.0891756i | \(0.0284232\pi\) | ||||
−0.996016 | + | 0.0891756i | \(0.971577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.89898 | + | 18.7980i | −0.0845035 | + | 0.836498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.3485i | 1.39223i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.4495 | −1.61560 | −0.807798 | − | 0.589460i | \(-0.799341\pi\) | ||||
−0.807798 | + | 0.589460i | \(0.799341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.89898 | 0.305193 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.89898 | − | 0.696938i | −0.304005 | − | 0.0307108i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.40408i | 0.193691i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.6969 | −1.96198 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.30306 | 0.144710 | 0.0723549 | − | 0.997379i | \(-0.476949\pi\) | ||||
0.0723549 | + | 0.997379i | \(0.476949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.14643i | 0.0501298i | 0.999686 | + | 0.0250649i | \(0.00797924\pi\) | ||||
−0.999686 | + | 0.0250649i | \(0.992021\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.0000 | − | 2.44949i | −0.523723 | − | 0.106904i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.79796i | − | 0.0783203i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.5959 | −1.06939 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.3485 | 0.839652 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.89898i | 0.212198i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.7980 | + | 1.79796i | 0.769473 | + | 0.0777325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 14.2020i | − | 0.612863i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.89898 | 0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.5959 | 1.27243 | 0.636214 | − | 0.771513i | \(-0.280500\pi\) | ||||
0.636214 | + | 0.771513i | \(0.280500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 34.8990i | − | 1.49766i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.651531 | + | 6.44949i | −0.0279085 | + | 0.276266i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.6969i | − | 0.457368i | −0.973501 | − | 0.228684i | \(-0.926558\pi\) | ||
0.973501 | − | 0.228684i | \(-0.0734423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.3485 | 1.08185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.6969 | −0.796516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.89898i | − | 0.123277i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.10102 | − | 10.8990i | 0.0467357 | − | 0.462636i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6969i | 0.707472i | 0.935345 | + | 0.353736i | \(0.115089\pi\) | ||||
−0.935345 | + | 0.353736i | \(0.884911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0454i | 0.591943i | 0.955197 | + | 0.295972i | \(0.0956434\pi\) | ||||
−0.955197 | + | 0.295972i | \(0.904357\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.449490 | − | 0.0454077i | −0.0189102 | − | 0.00191032i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000i | 0.377964i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.2020 | −0.595381 | −0.297690 | − | 0.954663i | \(-0.596216\pi\) | ||||
−0.297690 | + | 0.954663i | \(0.596216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8990 | 0.874595 | 0.437298 | − | 0.899317i | \(-0.355936\pi\) | ||||
0.437298 | + | 0.899317i | \(0.355936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 40.8990i | − | 1.70858i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89898 | − | 33.7980i | 0.287707 | − | 1.40947i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.4949i | 1.93561i | 0.251705 | + | 0.967804i | \(0.419009\pi\) | ||||
−0.251705 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.1010 | 1.79122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.44949 | 0.101622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.39388i | 0.223392i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | + | 0.303062i | 0.124035 | + | 0.0125301i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.1464i | 1.36810i | 0.729435 | + | 0.684050i | \(0.239783\pi\) | ||||
−0.729435 | + | 0.684050i | \(0.760217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79796 | −0.238901 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.2929 | 0.917006 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.10102i | 0.0452135i | 0.999744 | + | 0.0226067i | \(0.00719656\pi\) | ||||
−0.999744 | + | 0.0226067i | \(0.992803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.449490 | − | 4.44949i | 0.0184273 | − | 0.182411i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 17.3939i | − | 0.711884i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8990 | 0.935627 | 0.467813 | − | 0.883827i | \(-0.345042\pi\) | ||||
0.467813 | + | 0.883827i | \(0.345042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3939 | 0.791093 | 0.395546 | − | 0.918446i | \(-0.370555\pi\) | ||||
0.395546 | + | 0.918446i | \(0.370555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 24.0000i | − | 0.977356i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.92168 | − | 28.9217i | 0.118783 | − | 1.17583i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.3939i | − | 1.03071i | −0.856978 | − | 0.515353i | \(-0.827661\pi\) | ||
0.856978 | − | 0.515353i | \(-0.172339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.10102 | −0.287748 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.404082 | −0.0163474 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.20204i | − | 0.331277i | −0.986187 | − | 0.165639i | \(-0.947031\pi\) | ||
0.986187 | − | 0.165639i | \(-0.0529685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −59.3939 | − | 6.00000i | −2.39499 | − | 0.241943i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.59592i | − | 0.386317i | −0.981168 | − | 0.193159i | \(-0.938127\pi\) | ||
0.981168 | − | 0.193159i | \(-0.0618732\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.4495 | −1.86696 | −0.933481 | − | 0.358626i | \(-0.883245\pi\) | ||||
−0.933481 | + | 0.358626i | \(0.883245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 10.0000i | − | 0.400642i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 77.3939i | − | 3.09081i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.49490 | 0.258558 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 29.3939i | − | 1.16830i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.3485 | − | 1.14643i | −0.450350 | − | 0.0454946i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.449490i | 0.0178094i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.6969 | 1.29347 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.20204 | 0.244966 | 0.122483 | − | 0.992471i | \(-0.460914\pi\) | ||||
0.122483 | + | 0.992471i | \(0.460914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.14643i | − | 0.360700i | −0.983603 | − | 0.180350i | \(-0.942277\pi\) | ||
0.983603 | − | 0.180350i | \(-0.0577230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.89898 | + | 48.4949i | −0.192897 | + | 1.90948i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.2929i | 0.876423i | 0.898872 | + | 0.438211i | \(0.144388\pi\) | ||||
−0.898872 | + | 0.438211i | \(0.855612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5959 | 1.24025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.20204 | −0.0863048 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 39.7980i | − | 1.55741i | −0.627387 | − | 0.778707i | \(-0.715876\pi\) | ||
0.627387 | − | 0.778707i | \(-0.284124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.348469 | − | 3.44949i | 0.0136158 | − | 0.134783i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 20.6969i | − | 0.807464i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.10102 | 0.276616 | 0.138308 | − | 0.990389i | \(-0.455834\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9444 | −0.503478 | −0.251739 | − | 0.967795i | \(-0.581003\pi\) | ||||
−0.251739 | + | 0.967795i | \(0.581003\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.20204i | 0.0855202i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.3485 | − | 1.44949i | −0.556410 | − | 0.0562088i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.0000i | − | 0.774403i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.79796 | −0.378811 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.3939 | 1.59799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.79796i | − | 0.0693062i | −0.999399 | − | 0.0346531i | \(-0.988967\pi\) | ||
0.999399 | − | 0.0346531i | \(-0.0110326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.5505i | 1.21258i | 0.795242 | + | 0.606292i | \(0.207344\pi\) | ||||
−0.795242 | + | 0.606292i | \(0.792656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.79796 | −0.145752 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 35.5959i | − | 1.36204i | −0.732265 | − | 0.681020i | \(-0.761537\pi\) | ||
0.732265 | − | 0.681020i | \(-0.238463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.5959 | + | 4.00000i | 1.51288 | + | 0.152832i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.1010i | 1.41549i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.494897 | −0.0188541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1464 | 0.500114 | 0.250057 | − | 0.968231i | \(-0.419551\pi\) | ||||
0.250057 | + | 0.968231i | \(0.419551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 14.6969i | − | 0.558291i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.44949 | − | 14.3485i | 0.0549823 | − | 0.544268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 21.7980i | − | 0.825657i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.9898 | 0.945201 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.6969 | −1.53710 | −0.768551 | − | 0.639788i | \(-0.779022\pi\) | ||||
−0.768551 | + | 0.639788i | \(0.779022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.8990i | − | 0.486494i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.494897 | − | 4.89898i | 0.0186389 | − | 0.184506i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.44949i | 0.317776i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2929 | 1.51323 | 0.756615 | − | 0.653861i | \(-0.226852\pi\) | ||||
0.756615 | + | 0.653861i | \(0.226852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69694 | −0.326161 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.20204i | − | 0.232268i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.89898 | + | 0.494897i | 0.183211 | + | 0.0185081i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63.1918i | 2.35994i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.4949 | −1.65938 | −0.829690 | − | 0.558225i | \(-0.811483\pi\) | ||||
−0.829690 | + | 0.558225i | \(0.811483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.10102 | −0.115488 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.6969i | 1.88544i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.2020 | + | 2.89898i | 0.527451 | + | 0.107665i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.69694i | − | 0.248376i | −0.992259 | − | 0.124188i | \(-0.960367\pi\) | ||
0.992259 | − | 0.124188i | \(-0.0396325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7980 | −0.658281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.6413i | − | 1.61193i | −0.591964 | − | 0.805965i | \(-0.701647\pi\) | ||
0.591964 | − | 0.805965i | \(-0.298353\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.44949 | − | 0.550510i | −0.201007 | − | 0.0203059i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 39.1918i | − | 1.44365i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.4949 | −1.63677 | −0.818386 | − | 0.574669i | \(-0.805131\pi\) | ||||
−0.818386 | + | 0.574669i | \(0.805131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.10102 | 0.260863 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3031i | 0.561415i | 0.959793 | + | 0.280707i | \(0.0905691\pi\) | ||||
−0.959793 | + | 0.280707i | \(0.909431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.55051 | − | 35.1464i | 0.130081 | − | 1.28767i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.34847i | − | 0.268866i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2020 | −0.810164 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.79796i | 0.138405i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.40408 | + | 43.5959i | −0.160281 | + | 1.58662i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2020i | 1.17040i | 0.810888 | + | 0.585202i | \(0.198985\pi\) | ||||
−0.810888 | + | 0.585202i | \(0.801015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 82.7878 | 3.00501 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8990 | −1.12009 | −0.560044 | − | 0.828463i | \(-0.689216\pi\) | ||||
−0.560044 | + | 0.828463i | \(0.689216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.89898i | 0.104950i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.3485 | − | 1.34847i | −0.482615 | − | 0.0487540i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.89898i | 0.104676i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3031 | 0.407599 | 0.203799 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203799 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.6969 | −1.82581 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13.3485i | − | 0.480111i | −0.970759 | − | 0.240056i | \(-0.922834\pi\) | ||
0.970759 | − | 0.240056i | \(-0.0771657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.40408 | + | 0.898979i | 0.158199 | + | 0.0322923i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.89898i | − | 0.175750i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −70.2929 | −2.51850 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.3939 | 1.91058 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.7980 | − | 1.89898i | −0.670928 | − | 0.0677775i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.5505i | − | 1.62370i | −0.583866 | − | 0.811850i | \(-0.698461\pi\) | ||
0.583866 | − | 0.811850i | \(-0.301539\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.202041 | −0.00718375 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79796i | 0.134869i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.606123 | − | 6.00000i | 0.0214970 | − | 0.212798i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 52.9444i | − | 1.87539i | −0.347464 | − | 0.937693i | \(-0.612957\pi\) | ||
0.347464 | − | 0.937693i | \(-0.387043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.79796 | 0.0636072 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 33.7980i | − | 1.19270i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.55051 | − | 15.3485i | 0.0546483 | − | 0.540962i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 37.1010i | − | 1.30602i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.40408 | −0.295472 | −0.147736 | − | 0.989027i | \(-0.547199\pi\) | ||||
−0.147736 | + | 0.989027i | \(0.547199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.9444 | 1.36752 | 0.683761 | − | 0.729706i | \(-0.260343\pi\) | ||||
0.683761 | + | 0.729706i | \(0.260343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.3939i | 1.03089i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.5959 | − | 3.79796i | −1.31693 | − | 0.133037i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.3939i | 2.00796i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.34847 | 0.0471193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.7980 | −0.970155 | −0.485078 | − | 0.874471i | \(-0.661209\pi\) | ||||
−0.485078 | + | 0.874471i | \(0.661209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.1918i | − | 1.36614i | −0.730352 | − | 0.683071i | \(-0.760644\pi\) | ||
0.730352 | − | 0.683071i | \(-0.239356\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 58.7878i | −0.417786 | + | 2.04673i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.5959i | − | 0.820510i | −0.911971 | − | 0.410255i | \(-0.865440\pi\) | ||
0.911971 | − | 0.410255i | \(-0.134560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.6413 | 1.37680 | 0.688400 | − | 0.725331i | \(-0.258313\pi\) | ||||
0.688400 | + | 0.725331i | \(0.258313\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4949 | −0.433443 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.00000i | − | 0.0692959i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8990 | + | 1.10102i | 0.377175 | + | 0.0381024i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.1010 | −0.935631 | −0.467816 | − | 0.883826i | \(-0.654959\pi\) | ||||
−0.467816 | + | 0.883826i | \(0.654959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 44.0908i | − | 1.51857i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.87628 | − | 28.4722i | 0.0989469 | − | 0.979473i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.0000i | − | 0.446685i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −69.1918 | −2.37466 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.7980 | 0.472988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8434i | 1.02182i | 0.859635 | + | 0.510909i | \(0.170691\pi\) | ||||
−0.859635 | + | 0.510909i | \(0.829309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.34847 | + | 43.0454i | −0.148715 | + | 1.47212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.1918i | 0.860537i | 0.902701 | + | 0.430268i | \(0.141581\pi\) | ||||
−0.902701 | + | 0.430268i | \(0.858419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.6413 | −1.01135 | −0.505674 | − | 0.862724i | \(-0.668756\pi\) | ||||
−0.505674 | + | 0.862724i | \(0.668756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.6969 | −0.909829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.3939i | − | 0.455933i | −0.973669 | − | 0.227966i | \(-0.926792\pi\) | ||
0.973669 | − | 0.227966i | \(-0.0732076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.5959 | + | 4.10102i | 1.38030 | + | 0.139439i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.8434i | 1.08146i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.2020 | −0.481771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.59592 | 0.121843 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.3939i | 0.385624i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.6742 | + | 3.32577i | 0.360855 | + | 0.112431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 19.3939i | − | 0.654885i | −0.944871 | − | 0.327442i | \(-0.893813\pi\) | ||
0.944871 | − | 0.327442i | \(-0.106187\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.3031 | 0.516159 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7980 | 0.936537 | 0.468269 | − | 0.883586i | \(-0.344878\pi\) | ||||
0.468269 | + | 0.883586i | \(0.344878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.7980i | 1.40661i | 0.710887 | + | 0.703307i | \(0.248294\pi\) | ||||
−0.710887 | + | 0.703307i | \(0.751706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.1464 | − | 3.55051i | −1.18143 | − | 0.119349i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 26.6969i | − | 0.896395i | −0.893934 | − | 0.448198i | \(-0.852066\pi\) | ||
0.893934 | − | 0.448198i | \(-0.147934\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.10102 | −0.171083 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0908 | 1.47710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.79796i | − | 0.194021i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.30306 | + | 12.8990i | −0.0435565 | + | 0.431165i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.59592i | 0.253620i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.60612 | 0.0869191 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20204 | 0.0733606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.7980i | 0.725391i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.20204 | + | 31.6969i | −0.106439 | + | 1.05364i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.2020i | 0.737207i | 0.929587 | + | 0.368603i | \(0.120164\pi\) | ||||
−0.929587 | + | 0.368603i | \(0.879836\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.3485 | 0.840756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59592 | 0.119138 | 0.0595690 | − | 0.998224i | \(-0.481027\pi\) | ||||
0.0595690 | + | 0.998224i | \(0.481027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.0454 | − | 4.65153i | −1.52221 | − | 0.153775i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.55051i | − | 0.0512024i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1010 | 0.564111 | 0.282055 | − | 0.959398i | \(-0.408984\pi\) | ||||
0.282055 | + | 0.959398i | \(0.408984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.4041 | 0.342826 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.89898i | 0.161252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | + | 9.79796i | −0.0657596 | + | 0.322155i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.30306i | 0.305553i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.2929 | −1.32197 | −0.660983 | − | 0.750401i | \(-0.729860\pi\) | ||||
−0.660983 | + | 0.750401i | \(0.729860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.44949 | −0.211373 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.3939i | 0.962312i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.7980 | − | 2.20204i | −0.712869 | − | 0.0720144i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.8990i | − | 1.66280i | −0.555677 | − | 0.831399i | \(-0.687541\pi\) | ||
0.555677 | − | 0.831399i | \(-0.312459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.1010 | 1.40655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4495 | 0.797031 | 0.398515 | − | 0.917162i | \(-0.369526\pi\) | ||||
0.398515 | + | 0.917162i | \(0.369526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 75.1918i | − | 2.44858i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.0908i | 1.43276i | 0.697711 | + | 0.716379i | \(0.254202\pi\) | ||||
−0.697711 | + | 0.716379i | \(0.745798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.10102 | 0.100663 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 64.8990 | 2.10449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.7980i | − | 0.706105i | −0.935603 | − | 0.353053i | \(-0.885144\pi\) | ||
0.935603 | − | 0.353053i | \(-0.114856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.75255 | + | 37.1464i | −0.121430 | + | 1.20203i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.7878i | 1.12453i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7980 | 0.574726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1918 | −0.973930 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 24.0000i | − | 0.773389i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.1464 | − | 3.95459i | −1.26017 | − | 0.127303i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2929i | 1.03847i | 0.854632 | + | 0.519234i | \(0.173783\pi\) | ||||
−0.854632 | + | 0.519234i | \(0.826217\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.5959 | −1.01501 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.4495 | 0.463706 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.44949i | − | 0.206761i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.39388 | − | 1.10102i | −0.172742 | − | 0.0352609i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3939i | 0.940393i | 0.882562 | + | 0.470197i | \(0.155817\pi\) | ||||
−0.882562 | + | 0.470197i | \(0.844183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.9898 | −1.56572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.69694 | 0.277672 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.6969i | 1.36182i | 0.732367 | + | 0.680910i | \(0.238416\pi\) | ||||
−0.732367 | + | 0.680910i | \(0.761584\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.2474 | − | 2.04541i | −0.645137 | − | 0.0651721i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.20204i | − | 0.0700917i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61.3939 | −1.95221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.6969 | 1.92810 | 0.964051 | − | 0.265718i | \(-0.0856089\pi\) | ||||
0.964051 | + | 0.265718i | \(0.0856089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 26.2020i | − | 0.831497i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59592 | + | 15.7980i | −0.0505940 | + | 0.500829i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.6515i | − | 1.35079i | −0.737457 | − | 0.675394i | \(-0.763974\pi\) | ||
0.737457 | − | 0.675394i | \(-0.236026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2240.2.g.j.449.4 | 4 | ||
4.3 | odd | 2 | 2240.2.g.i.449.2 | 4 | |||
5.4 | even | 2 | inner | 2240.2.g.j.449.2 | 4 | ||
8.3 | odd | 2 | 560.2.g.e.449.3 | 4 | |||
8.5 | even | 2 | 70.2.c.a.29.1 | ✓ | 4 | ||
20.19 | odd | 2 | 2240.2.g.i.449.4 | 4 | |||
24.5 | odd | 2 | 630.2.g.g.379.4 | 4 | |||
24.11 | even | 2 | 5040.2.t.t.1009.3 | 4 | |||
40.3 | even | 4 | 2800.2.a.bm.1.1 | 2 | |||
40.13 | odd | 4 | 350.2.a.g.1.2 | 2 | |||
40.19 | odd | 2 | 560.2.g.e.449.1 | 4 | |||
40.27 | even | 4 | 2800.2.a.bl.1.2 | 2 | |||
40.29 | even | 2 | 70.2.c.a.29.4 | yes | 4 | ||
40.37 | odd | 4 | 350.2.a.h.1.1 | 2 | |||
56.5 | odd | 6 | 490.2.i.f.459.1 | 8 | |||
56.13 | odd | 2 | 490.2.c.e.99.2 | 4 | |||
56.37 | even | 6 | 490.2.i.c.459.2 | 8 | |||
56.45 | odd | 6 | 490.2.i.f.79.4 | 8 | |||
56.53 | even | 6 | 490.2.i.c.79.3 | 8 | |||
120.29 | odd | 2 | 630.2.g.g.379.2 | 4 | |||
120.53 | even | 4 | 3150.2.a.bt.1.1 | 2 | |||
120.59 | even | 2 | 5040.2.t.t.1009.4 | 4 | |||
120.77 | even | 4 | 3150.2.a.bs.1.1 | 2 | |||
280.13 | even | 4 | 2450.2.a.bl.1.1 | 2 | |||
280.69 | odd | 2 | 490.2.c.e.99.3 | 4 | |||
280.109 | even | 6 | 490.2.i.c.79.2 | 8 | |||
280.149 | even | 6 | 490.2.i.c.459.3 | 8 | |||
280.229 | odd | 6 | 490.2.i.f.459.4 | 8 | |||
280.237 | even | 4 | 2450.2.a.bq.1.2 | 2 | |||
280.269 | odd | 6 | 490.2.i.f.79.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.c.a.29.1 | ✓ | 4 | 8.5 | even | 2 | ||
70.2.c.a.29.4 | yes | 4 | 40.29 | even | 2 | ||
350.2.a.g.1.2 | 2 | 40.13 | odd | 4 | |||
350.2.a.h.1.1 | 2 | 40.37 | odd | 4 | |||
490.2.c.e.99.2 | 4 | 56.13 | odd | 2 | |||
490.2.c.e.99.3 | 4 | 280.69 | odd | 2 | |||
490.2.i.c.79.2 | 8 | 280.109 | even | 6 | |||
490.2.i.c.79.3 | 8 | 56.53 | even | 6 | |||
490.2.i.c.459.2 | 8 | 56.37 | even | 6 | |||
490.2.i.c.459.3 | 8 | 280.149 | even | 6 | |||
490.2.i.f.79.1 | 8 | 280.269 | odd | 6 | |||
490.2.i.f.79.4 | 8 | 56.45 | odd | 6 | |||
490.2.i.f.459.1 | 8 | 56.5 | odd | 6 | |||
490.2.i.f.459.4 | 8 | 280.229 | odd | 6 | |||
560.2.g.e.449.1 | 4 | 40.19 | odd | 2 | |||
560.2.g.e.449.3 | 4 | 8.3 | odd | 2 | |||
630.2.g.g.379.2 | 4 | 120.29 | odd | 2 | |||
630.2.g.g.379.4 | 4 | 24.5 | odd | 2 | |||
2240.2.g.i.449.2 | 4 | 4.3 | odd | 2 | |||
2240.2.g.i.449.4 | 4 | 20.19 | odd | 2 | |||
2240.2.g.j.449.2 | 4 | 5.4 | even | 2 | inner | ||
2240.2.g.j.449.4 | 4 | 1.1 | even | 1 | trivial | ||
2450.2.a.bl.1.1 | 2 | 280.13 | even | 4 | |||
2450.2.a.bq.1.2 | 2 | 280.237 | even | 4 | |||
2800.2.a.bl.1.2 | 2 | 40.27 | even | 4 | |||
2800.2.a.bm.1.1 | 2 | 40.3 | even | 4 | |||
3150.2.a.bs.1.1 | 2 | 120.77 | even | 4 | |||
3150.2.a.bt.1.1 | 2 | 120.53 | even | 4 | |||
5040.2.t.t.1009.3 | 4 | 24.11 | even | 2 | |||
5040.2.t.t.1009.4 | 4 | 120.59 | even | 2 |